Properties

Modulus $161$
Structure \(C_{66}\times C_{2}\)
Order $132$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(161)
 
pari: g = idealstar(,161,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 132
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{66}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{161}(24,\cdot)$, $\chi_{161}(120,\cdot)$

First 32 of 132 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{161}(1,\cdot)\) 161.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{161}(2,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{161}(3,\cdot)\) 161.n 66 yes \(-1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{25}{66}\right)\)
\(\chi_{161}(4,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{161}(5,\cdot)\) 161.o 66 yes \(1\) \(1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{5}{66}\right)\)
\(\chi_{161}(6,\cdot)\) 161.l 22 yes \(-1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{161}(8,\cdot)\) 161.i 11 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{161}(9,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{161}(10,\cdot)\) 161.o 66 yes \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{161}(11,\cdot)\) 161.p 66 yes \(-1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{161}(12,\cdot)\) 161.n 66 yes \(-1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{161}(13,\cdot)\) 161.l 22 yes \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{161}(15,\cdot)\) 161.j 22 no \(-1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{161}(16,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{161}(17,\cdot)\) 161.o 66 yes \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{161}(18,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{161}(19,\cdot)\) 161.o 66 yes \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{53}{66}\right)\)
\(\chi_{161}(20,\cdot)\) 161.k 22 yes \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{161}(22,\cdot)\) 161.d 2 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{161}(24,\cdot)\) 161.h 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{161}(25,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{161}(26,\cdot)\) 161.n 66 yes \(-1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{47}{66}\right)\)
\(\chi_{161}(27,\cdot)\) 161.l 22 yes \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{161}(29,\cdot)\) 161.i 11 no \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{161}(30,\cdot)\) 161.p 66 yes \(-1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{161}(31,\cdot)\) 161.n 66 yes \(-1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{19}{66}\right)\)
\(\chi_{161}(32,\cdot)\) 161.m 33 yes \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{161}(33,\cdot)\) 161.o 66 yes \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{59}{66}\right)\)
\(\chi_{161}(34,\cdot)\) 161.k 22 yes \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{161}(36,\cdot)\) 161.i 11 no \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{161}(37,\cdot)\) 161.p 66 yes \(-1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{161}(38,\cdot)\) 161.o 66 yes \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{19}{66}\right)\)